# Connection Oriented Networks - Perros H.G

ISBN 0-470-02163-2

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b. What is the peak and average transmission rate of the voice source including the overheads

due to the CPS-packet, the CPS-PDU and the ATM cell, assuming one CPS-packet per

CPS-PDU?

3. Consider an on/off source where the off period is constant and equal to 0.5 msec. The MBS of the source is 24 cells. During the on period, the source transmits at the rate of 20 Mbps.

a. What is its PCR?

b. What is the maximum length of the on period in msec?

c. Assuming a 1-msec period, calculate its SCR.

4. Explain why the end-to-end cell transfer delay consists of a fixed part and a variable part. What is the fixed part equal to?

5. Explain why jitter is important to a delay-sensitive applications.

6. Consider an on/off source with a peak bit rate = 500 Kbps, and an average on period = 100 msec. The source will be transmitted over the output port of a non-blocking switch, which has a buffer K = 500 cells. Plot the average bit rate and the equivalent bandwidth of the source as a function of r (i.e., the fraction of time that the source is active). You should observe that the equivalent bandwidth tends to its peak bit rate when the source is bursty and to its average bit rate when the source is regular (i.e. not bursty). (Remember to express K in bits!)

7. Consider the virtual scheduling algorithm for policing the PCR. Assume that T (1/PCR) = 40 units of time and the CDVT = 60 units of time. The arrival times are: 0, 45, 90, 120, 125, 132, 140, and 220. Which of these arrivals will get tagged?

8. Repeat Problem 7 using the continuous state leaky bucket algorithm.

APPENDIX: SIMULATION PROJECT: ATM TRAFFIC CHARACTERIZATION OF AN MPEG VIDEO SOURCE

An MPEG video encoder generates frames which are transmitted over an ATM link. Write a program to simulate the traffic generated by the MPEG video encoder with a view to characterizing the resulting ATM traffic.

Problem Description

An MPEG video encoder generates frames whose size is correlated and can be predicted using an autoregressive integrated moving average (ARIMA) model. As described in Section 4.1.3, for the group of pictures IBBPBBPBBPBB, the following ARIMA model can be used to predict the size S(i) of the ith frame in bits: S(i) = S(i — 12) + e(i) — 0.69748e(i — 3), where e(i) is white noise and it follows the distribution N(0, a2), with a2 = 4849.5 bits.

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CONGESTION CONTROL IN ATM NETWORKS

An MPEG (I, B, or P) frame is generated every 30 msec. The information generated for each frame is transmitted over an ATM link using AAL1 unstructured PDUs. Assume that it takes zero time to pack the bits of a frame into AAL1 PDUs and subsequently into ATM cells. Also, assume that the ATM cells generated by a single frame are transmitted out back-to-back over a slotted link, with a slot equal to 3 ^sec.

Assume that you are observing the ATM cells transmitted out on this slotted link. Due to the nature of the application, you will see that the ATM traffic behaves like an on/off model. Measure the following parameters of this ATM traffic: average cell rate, sustained cell rate with T = 900 msec, MBS, average off period, and the squared coefficient of variation of the inter-arrival c2.

Simulation Structure

The simulation program can be organized into three parts. In the first part, you generate the size of the next frame, and in the second part you collect statistics on the ATM cells generated by this frame. Repeat these two parts until you have generated 5000 frames. Then go to Part 3 to calculate and print the final statistics.

Part 1

Use the above auto-regressive model to generate the size in bits of the next frame. For this, you will need to keep the size of the previous twelve frames. Start generating from frame 13 using the following initial values, expressed in bits: 5(1) = 999700, S(2) = 97600, S(3) = 395500, S(4) = 516460, S(5) = 89840, S(6) = 295500, S(7) = 696820, S(8) = 77900, S(9) = 89840, S(10) = 619220, S(11) = 97300, S(12) = 95360.

Use the following procedure to generate Normally distributed variates for e(i):

1. Draw two random numbers r1 and r2, 0 < rbr2 < 1.

Calculate v = 2r1 — 1, è = 2r2 — 1, and w = v2 + u2.

2. If w > 1, then repeat Step 1; otherwise, x = v [(—2logew)/w]1/2.

3. Set e (i) = 69.638x.

Part 2

A new frame is generated every 30 msec. Having generated the frame size, calculate how many ATM cells are required to carry this frame. Let X be the number of required ATM cells. These ATM cells are generated instantaneously, and are transmitted out back-to-back, with a transmission time equal to 3 ^sec per cell. Calculate how many slots will be idle before the next frame arrives. Let the number of idle slots be Y. Update the following variables:

frame_counter = frame_counter + 1 total_simulation_time = total_simulation_time + 30 totalcellsarrived = totalcellsarrived + X MBS = max{MBS, X} on_period = on_period + X off_period = off_period + Y

APPENDIX: SIMULATION PROJECT: ATM TRAFFIC CHARACTERIZATION

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